Direction vectors are d1=(1,2,2) with magnitude 3, and d2=(3,2,6) with magnitude 7. Dot product =3+4+12=19. So cosθ=19/(3⋅7)=19/21, giving θ=cos−1(19/21).
The angle between the lines r=3i^+2j^−4k^+λ(i^+2j^+2k^) and r=5j^−2k^+μ(3i^+2j^+6k^) is :
Held on 23 May 2023 · Verified 13 Jul 2026.
sin−1(2119)
cos−1(2319)
cos−1(2119)
sin−1(2319)
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The shortest distance between the following lines: $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + s(2\hat{i} + \hat{j} + \hat{k})$ $\vec{r} = (\hat{i} + \hat{j} + 2\hat{k}) + t(4\hat{i} + 2\hat{j} + 2\hat{k})$, where s and t are scalars, is:
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